The shadow defence secretary, Maria Eagle, led the charge as she described Corbyn’s comments as unhelpful – prompting a rebuke in turn from Diane Abbott, the shadow international development secretary.

A succession of shadow cabinet ministers – Andy Burnham, Hilary Benn, Angela Eagle, Lord Falconer and Heidi Alexander – all threw their weight behind the shadow defence secretary as they warned that it would be wrong to rule out the use of Trident missiles in all circumstances.

Sir Paul Kenny, the general secretary of the GMB union, suggested that Corbyn might have to resign as prime minister if he declined to authorise the use of nuclear weapons.

The row began on Wednesday morning when the Labour leader told the Today programme on BBC Radio 4 that he would, as prime minister, make it clear to the heads of the armed forces that he would never authorise the use of Trident. Asked if he would use nuclear weapons, he said: “No.”

Corbyn added: “There are five declared nuclear weapon states in the world. There are three others that have nuclear weapons. That is eight countries out of 192; 187 countries do not feel the need to have nuclear weapons to protect their security. Why should those five need them to protect their security? We are not in the cold war any more.

Jeremy Corbyn: ‘It’s wrong to spend £100bn on Trident.’

“I don’t think we should be spending £100bn on renewing Trident. That is a quarter of our defence budget. There are many in the military that do not want Trident renewed because they see it as an obsolete thing they don’t need. They would much rather see it spent on conventional weapons.”

Maria Eagle criticised Corbyn’s remarks. She told the BBC: “It undermines to some degree our attempt to try and get a policy process going. As far as I am concerned, we start from the policy we have. I don’t think that a potential prime minister answering a question like that in the way he did is helpful.”

A series of Eagle’s colleagues supported her in interviews with the BBC. Asked whether prime ministers should always have the option of using nuclear weapons as a last resort, Burnham, the shadow home secretary, said: “I think so, I do, because if a deterrent is to mean what it says then that is an option that prime ministers have to keep.”

The shadow foreign secretary, Hilary Benn, said: “I think a British prime minister has to have that option. The whole purpose of the deterrent, of course, is it is trying to deter a potential enemy.”

Angela Eagle, the shadow business secretary, said: “I don’t think anyone in their right mind would want to get into a situation where it would be used. But if you do get to that situation you have to be prepared to use it.”

Falconer, the shadow justice secretary, said: “If you’ve got a nuclear deterrent you have got to be willing to use it in extreme circumstances or it isn’t a deterrent.”

Alexander, the shadow health secretary, said: “You should never say never in politics because what you need to do is look at the circumstances that arise, the evidence before you.”

David Cameron said Corbyn’s comments showed that Labour could not be trusted with the nation’s security.

Speaking in Jamaica, where he is on an official visit, the prime minister said: “The independent nuclear deterrent that we have in Britain is a vital insurance policy for our nation in what is a very dangerous world.

“The way the Labour leader has answered that question undermines our deterrent and demonstrates that Labour can’t be trusted with our national security, which after all is the most important duty of government.”

The row meant that the Labour conference ended on a difficult note. But the differences over Trident, which are to be examined in a review headed by Maria Eagle, go to the heart of the debate about the future of the Labour party.

Eagle and a host of other shadow cabinet ministers including Benn and the deputy leader, Tom Watson, believe that supporting Trident renewal is a vital part of assuring centrist voters that the nation’s security would be safe in Labour’s hands.

Corbyn and his close ally John McDonnell, who are longstanding supporters of the Campaign for Nuclear Disarmament from their earliest days in politics in the 1960s, regard their opposition to Trident as a red line.

The Labour leader, who says his support for unilateral disarmament is one of his defining political beliefs, responded to the row by pointing out that US nuclear weapons did not prevent the 9/11 terror attacks.

The Labour leader told the BBC: “The nuclear weapons the US holds – all the hundreds, if not thousands of weapons they have got – were no help to them on 9/11. The issues are threats of irrational acts by individuals.”

The open defiance by Maria Eagle shows that the shadow cabinet faces a bumpy ride after Corbyn told the conference he would use his “huge mandate” in the leadership contest to change the party’s position. Corbyn failed this week to hold a vote on whether to continue supporting the renewal of Trident.

The Labour leader later told ITV News that he would “live with it somehow” if he failed to change party policy.

Shadow ministers who support the renewal of Trident say that Eagle’s review is likely to deliver a predictable result: that the party is divided and it is all but impossible to see how the opposing camps can reconcile their views. Corbyn’s failure to hold a vote on Trident, after failing to win union support, means he will struggle to change party policy.

The supporters of nuclear weapons were encouraged by Kenny, who suggested that Corbyn would have to consider resigning if he refused to back Trident while Labour was still formally committed to the programme.

The union leader told the BBC’s World at One: “Then he’s got a choice to make in terms of whether he followed the defence policy of the country, or felt that he should resign. His integrity would drive his decision one way or another.”

Kenny’s remarks are designed to avoid a scenario in which Corbyn became prime minister as leader of a party that officially supported the Trident programme. In such circumstances Corbyn would in effect have the ability to embark on disarmament on his first day in office because the prime minister is the sole person who exercises the royal prerogative – the monarch’s power to wage war and sign treaties.

Prime ministers can authorise nuclear strikes in two circumstances envisaged under the arrangements in place since the cold war. In the first instance, based on the assumption that the UK is still a functioning state, the chief of the defence staff recommends to the prime minister that nuclear weapons should be launched from a Vanguard-class submarine, one of which is always on patrol. The prime minister would have to accept this recommendation.

The second instance is based on the assumption that the UK is no longer a functioning state. In such circumstances, signalled when BBC Radio 4 can no longer be heard, the commander of the submarine on patrol would take a sealed letter, written by the prime minister, from a safe.

The letter is written on the day the prime minister is appointed and instructs the submarine commanders on what to do in the event of a nuclear strike on Britain.